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## Uguisudani Math

A cache by bebebe0622jp Message this owner
Hidden : 3/19/2008
Difficulty:
Terrain:

Size:  (micro)

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### Geocache Description:

Math puzzle micro near JR Uguisudani Station.

Fibonacci numbers are seen in nature, known as golden ratio.
Please calculate the coordinate of the real cache by using a slight math.
The definition of Fibonacci numbers is shown below.
F(0) = 0, F(1) = 1
F(n+2) = F(n) + F(n+1) (n >=0)

For example, the following numbers are shown below.
F(2) = 1, F(3) = 2, F(4) = 3, ....

Let's extend this definition.
I added superscript number shown below.
F(m)(0) = ... = F(m)(m-2) = 0, F(m)(m-1) = 1
F(m)(n+m) = F(m)(n) + F(m)(n+1) + ... + F(m)(n+m-1)

So, when m is equal to 2, F(2)(n) is "usual" Fibonacci sequence.

The real cache is located following coordinates.

N 35° 43.(F(2)(12) + F(3)(12) + 1)
E 139° 46.(F(6)(15) + F(5)(11))

The cache container is a card case. Bring your own writing. Additionally, please avoid putting in any Geocoin in the cache.

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### 112 Logged Visits

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